# Tagged Questions

**2**

votes

**0**answers

158 views

### Computing the chromatic polynomial of graph modulo $x-3$

The chromatic polynomial of graph $P(G,x)$ is univariate
polynomial which counts the number of colorings of $G$
with $x$ colors for natural $x$.
Graph is not $k$ colorable iff $P(G,k)=0$.
The ...

**3**

votes

**0**answers

39 views

### Algorithm to construct metric space endomorphism with controlled square

Given a finite metric space $(M,d)$ with parameters $K \geq 1$ and $\epsilon > 0$, I'd like to algorithmically check for the existence of a non-identity map $\phi:M \to M$ which happens to be ...

**7**

votes

**0**answers

90 views

### Algorithms for computing the Resilience of Graphs

The definition of resilience with a graph $G$ w.r.t to a monotone property $\mathcal{P}$ is well known.
(Global resilience) Let $\mathcal{P}$ be an increasing monotone property. The global ...

**-4**

votes

**1**answer

144 views

### Bipartite graph [closed]

First of all, thank you for your time to reading my post.
I am a researcher but not a mathematician, i have some difficulties in solving a math problem, that why i am here to ask your help. I just ...

**17**

votes

**0**answers

151 views

### A small unavoidable collection of subgraphs

What is the smallest number S(k,n) of unlabeled graphs on k vertices such that every simple graph on n vertices contains at least one of these as an induced subgraph?
I'd like to avoid exhaustive ...

**3**

votes

**1**answer

104 views

### A problem related to routing in a graph

I have come across a new problem - I want to know whether this problem is similar to some existing problem or not.
The new problem is this. There is a tourist who has a having the following ...

**1**

vote

**1**answer

78 views

### Is undirected short-simple-path-through-3-vertices decidable in polynomial time?

Consider the following language:
$L=\{\langle G=(V,E),s,v,t,l\rangle\;|\;s,v,t\in V, l\in \mathbb{N} \wedge $ There exists a simple path from $s$ to $t$, going through $v$ of length $\leq l\}$.
($G$ ...

**4**

votes

**4**answers

383 views

### Determine if a graph has a large clique

This question is quite specific and practical. I hope it is still relevant for MO and will not be removed.
I have a collection $\mathcal{C}$ of graphs having from 5000-6000 vertices and edge density ...

**2**

votes

**0**answers

57 views

### Smallest distribution of points with genuinely different clusterings

An hierarchical clustering algorithm for (finite) sets of points in a given metric space is essentially determined by its linkage criterion, which defines the distance between arbitrary (finite) sets ...

**4**

votes

**2**answers

139 views

### Details of generation programs supplied with nauty

The program nauty comes with gtools which contains, among others, several generation programs like geng, genbg, ... I was ...

**1**

vote

**4**answers

243 views

### Counting simple 4-cycles in an undirected graph [closed]

I'm looking for an algorithm which just counts the number of simple and distinct 4-cycles in an undirected graph labelled with integer keys. I don't need it to be optimal because I only have to use it ...

**6**

votes

**0**answers

139 views

### Uniformly sampling from the set of all simplicial maps

Let $K$ and $L$ be finite simplicial complexes that remain fixed throughout.
How does one efficiently sample (according to the uniform distribution) elements from the finite set of simplicial ...

**0**

votes

**1**answer

124 views

### Efficient isomorphic subgraph matching with similarity scores

I'm a computer vision PhD student, and I'm looking for an efficient approximation to the following problem, which could end up helping in image to image matching. Failing that, pointers to relevant ...

**0**

votes

**0**answers

68 views

### Minimum cut in near complete graph

I have a problem with an algorithm that i don't quite understand. The mathematics are not the problem, but I don't understand how it can work in practice. The problem is in the paper ...

**5**

votes

**5**answers

280 views

### Efficient Hamiltonian cycle algorithms for graph classes

Generally speaking finding a Hamiltonian cycle is NP-Hard and so tough. But if $G=L(H)$ is the line graph of $G$ then we can reduce the finding of a Hamiltonian cycle in $G$ to a Eurler your of $H$ ...

**20**

votes

**3**answers

1k views

### Can one measure the infeasibility of four color proofs?

Terms like "impractical" and "unfeasible" are used to say the Robertson, Sanders, Seymour, and Thomas proof of the four color theorem needs computer assistance. Obviously no precise measure is ...

**1**

vote

**1**answer

120 views

### Generating k-partite graphs

Does there exist an efficient algorithm for generating all non-isomorphic k-partite graphs up to a certain order $n$? I've read through the nauty tutorial, but it doesn't look like anything beyond ...

**2**

votes

**2**answers

206 views

### Geodesics in Graphs:Shortest Paths vs Going as Straight Ahead as Possible

According to Wikipedia http://en.wikipedia.org/wiki/Geodesic, a geodesic " is a generalization of the notion of a "straight line" to "curved spaces " and further " In the presence of an affine ...

**4**

votes

**2**answers

161 views

### Estimate size of graph by taking random walks

Let $G$ be a connected, finite graph and let $v_0$ be a vertex of $G$. I'm interested in methods of estimating the number of vertices in $G$, based on local exploration only. What I have in mind is:
...

**4**

votes

**0**answers

158 views

### Rough structure of the double coset space/Graph bijections up to automorphisms

I am dealing with bijective maps $\pi:\Gamma_1\to \Gamma_2$ between two graphs with the same number of vertices $N=O(10)$.
The graphs have a significant automorphism group (these are disconnected ...

**2**

votes

**3**answers

139 views

### Reference Request for: Finding Large Bipartite Subgraphs via Destruction of Odd Cycles in Graphs

From the observation, that a bipartite graph doesn't contain odd cycles, it would seem natural to attempt to destroy all odd cycles in the most efficient way, by either removing edges or vertices of ...

**3**

votes

**0**answers

171 views

### Beating Kadane's Algorithm

I am seeking some reference on already existing work for the following problem.
Given an $n$-dimensional square matrix $A=DP$ where $D$ is a diagonal and $P$ is a permutation matrix (think of Gaussian ...

**1**

vote

**1**answer

133 views

### What algorithms do you know for beltway reconstruction?

I've faced the beltway reconstruction problem and I've developed a simple backtrack algorithm, what algorithms do you know for this problem?
Beltway Reconstruction Problem:
Assume there is a set of ...

**5**

votes

**1**answer

452 views

### Difference Sets

Suppose
$$
P \subseteq \{1,2,\dots,N\},\quad |P| = K
$$
We calculate the differences as: $$d=p_i-p_j\mod N,\quad i\ne j$$
Now let $a_d$ denote the number of occurrence of $d$ (for $d = 1, 2, \dots , N ...

**6**

votes

**2**answers

194 views

### Recovering a Weighted Graph from Shortest Path Distances

I am interested in the following problem (A) and its related formulation (B).
(A) Suppose that $G = (V,E,w)$ is an unknown weighted graph on the vertex set $V$ and that one has access to $d_G(v,v'), ...

**1**

vote

**3**answers

213 views

### Strategic vertex labeling

We are given a graph $G=(V,E)$ with positive edge weights $w_{i}$ and numerical {0,1,-1} labels $l$ for all vertices . We know that $G$ has a subset $G'$ with all vertices labeled 0(all vertices with ...

**7**

votes

**0**answers

128 views

### How quickly can we test if a graph is distance-regular?

A (simple, finite, connected) graph $G$ is distance regular if there exist integers $b_i,c_i,i=0,...,D$ such that for any two vertices $x,y$ in $G$ and distance $i=d(x,y)$, there are exactly $c_i$ ...

**1**

vote

**1**answer

107 views

### Separation of Anti-Hole Inequality

Given an undirected graph $G=(V,E)$ with no loops or multiple edges, a stable set is a set of vertices for which no two vertices are adjacent.
An induced subgraph $H$ of $G$ is called an odd-antihole ...

**1**

vote

**0**answers

117 views

### regular hyper graph construction

Is there any algorithm to generate 3-uniform k-regular hypergraph with n vertices?? Any help is appreciated. Thanks.

**2**

votes

**1**answer

328 views

### Removing cycles from an undirected connected bipartite graph in a special manner

Consider an undirected connected bipartite graph (with cycles) $G = (V_1,V_2,E)$, where $V_1,V_2$ are the two node sets and $E$ is the set of edges connecting nodes in $V_1$ to those in $V_2$. We ...

**2**

votes

**1**answer

160 views

### algorithmic almost equitable partitioning

Let $G$ be a graph -- possibly infinite, but I will be glad to learn a positive result even in the finite case. Then the trivial partition (i.e., one cell coinciding with the whole $G$) is clearly ...

**2**

votes

**5**answers

858 views

### Algorithm to solve Sokoban-like game on graphs - move chips from one set of vertices to another

The question is close to the Sokoban game (thanks to Dima Pasechnik !), but a little different in details.
Consider a directed graph (multi-graph). Consider some set of marked chips (chip1, ...

**1**

vote

**0**answers

77 views

### Toroidality testing

Is there a standard test for the recognition of toroidal graphs?
I have been using the Boyer-Myrvold algorithm (which has a MATLAB implementation) and would like to know if there is something ...

**4**

votes

**1**answer

224 views

### Generating non-isomorphic graphs by adding edges to a given graph

Hello!
This question is in a way related to the one I posted on math.se. Since the question there did not produce any final answer I am trying my luck here!
I am given a fairly large graph $G$ and ...

**3**

votes

**1**answer

103 views

### Search for common substructures in list of graphs

I have had the following problem on several occasions and I was wondering whether there is a general technique to solve this problem.
Given a list of graphs with property $P$. Is there a general ...

**6**

votes

**1**answer

229 views

### Is it possible to decide in polynomial time if a poset is a subposet of another which is given ?

I am reading some theory on partial orders and I wonder something which perhaps has a simple answer : Given two partial orders $G_1,G_2$ (by their hasse diagrams), is it possible to know in ...

**0**

votes

**1**answer

484 views

### Finding the lowest cost set of disjoint paths using all nodes in a directed graph?

I have a directed graph with edges connecting nodes representing costs.
I wish to find the set of paths which
-go from node 'start' to node 'end'
-are node-disjoint (except for the start and end ...

**2**

votes

**0**answers

171 views

### A natural problem on “cartesian union” of set families (hypergraphs). Does anybody know NP-complete problems related to the notion of cartesian product?

I'm curious whether the problem below is NP-complete.
I provide two simple definitions and one example at first.
Definition 1.
Let $\langle {\cal{S}}_i\rangle\substack{i\in I}$ and $\langle ...

**0**

votes

**1**answer

249 views

### Counterexamples for this algorithm for recognizing lexicographic product of graphs?

Found a possible reduction from recognizing lexicographic product of graphs to 2SAT
(since 2SAT is polynomial, the algorithm is polynomial).
Can't prove completeness of the algorithm and since it is ...

**3**

votes

**2**answers

1k views

### Generation of All Path in a Directed Acyclic Graph

I am working on a very large dataset of a single DAG whose vertices have a low branching factor. I need to generate all possible (simple) paths starting from the source and write them to a file.
My ...

**10**

votes

**1**answer

583 views

### A generalization of the triangle counting problem for simple weighted graphs

One nice identity is $$tr(A^3)/6$$ which counts the number of triangles of a graph represented with adjacency matrix $A.$ It also implies that triangle counting can be performed in subcubic time.
...

**2**

votes

**0**answers

124 views

### Additional Constraint Baum Welch for HMMs

I'm trying to derive a special form of the Baum Welch algorithm where there is an additional constraint that the sum of emission probabilities over all states sums to one for each output symbol. ...

**10**

votes

**1**answer

240 views

### Network flows with capacities on pairs of edges

Take a standard network flow problem: a directed graph with nonnegative capacities on each edge, a source $s$, a sink $t$. We all know how to find the maximum flow from $s$ to $t$.
Now add edge-pair ...

**2**

votes

**1**answer

104 views

### A Parameter related to fractional chromatic number and Kneser Graphs

Let $t \gt 0$ be an integer and $G$ is a simple graph with $\chi_f(G) = t$. Then $t$= inf $\{ \frac{n}{k}| G \rightarrow KG(n,k)\}$ where $KG(n,k)$ is the Kneser graph.
Does there exist a $k$ such ...

**1**

vote

**1**answer

225 views

### Need input on a potentially NP-hard maximal edge-weighted multi-cycle graph

I've posted a question on Stack Overflow regarding a seemingly NP-hard problem on maximization of weighted cycles in a graph problem.
One of the respondents cited Professor David Speyer's Math ...

**1**

vote

**0**answers

66 views

### An MST-like problem with vertex selection

Consider a planar pointset in a rectangle, where every point has a color (an integer label).
We need to select one point of every color, so as to minimize the cost of a planar MST of selected points ...

**6**

votes

**0**answers

470 views

### Is Logical Min-Cut Problem, NP-Complete?

Logical Min Cut (LMC) Problem: Suppose that G = (V, E) is an unweighted digraph, s,t are two vertices of V, and t is reachable from s. LMC Problem states that how we can make t unreachable from s by ...

**2**

votes

**1**answer

104 views

### Do you know a shortes path algorithm for weighted graphs with hard time windows on the edges and waiting allowed?

Title says it all. I have a weighted Graph G={V,E,ETW} where V is the node set, E the edge set and ETW is a set of edge time windows. A edge time window is a 3-Tuple (edge, starttime, endtime) with ...

**1**

vote

**1**answer

190 views

### Shortest absolute value of path in graph

Suppose we have a weighted, acyclic digraph, with positive and negative edge weights.
Is there an algorithm that determines whether there is a path of weight zero between vertices A and B? The ...

**8**

votes

**0**answers

382 views

### Shortest path in Cayley graphs

The standard way to find the shortest path between 2 vertices, $v_1$ and $v_2$, of an undirected graph is BFS (breadth first search) which takes time $O(|E|)$ and space $O(|V|)$ (where $E$ is the set ...